Quantization
Quantization is a process of converting a free flowing sequence of values into specific buckets. In AI, this is used to convert large models weights to smaller values. This reduces the size of the model and makes it faster to run.
Quanta means discrete packets. The word was first coined when the flow of lights was discovered not to be continuous, instead it travels in packets called Quants.

The quantization doesn't happen to the entire weight matrix at once. The full weight matrix of a model is split into different blocks and then each block is quantized separately. Meaning, each block will have its own scale, min value, etc.
QAT
QAT stands for Quantization Aware Training. This is a process of training a model while keeping in mind that the weights will be quantized later on.
Optiq
This is just another technique, which doesn't quantize all layers with same quantization level. If it figures out that a specific layer adds more value, then it uses a higher quantization for such weights of such layer.